Answer :
Final answer:
Correct answer is b) .The overall average weight of all 100 students is calculated by finding the total weight of both groups and dividing by the total number of students, which results in an overall average weight of 162 pounds after rounding.
Explanation:
To determine the overall average weight of all 100 students, we need to take into account the average weights of the two groups and how many students are in each group. We start by finding the total weight of each group by multiplying the average weight by the number of students in that group.
The first group (3 students) has an average weight of 135 pounds:
- Total weight of group 1 = Average weight × Number of students = 135 pounds × 3 = 405 pounds
The second group (97 students) has an average weight of 163 pounds:
- Total weight of group 2 = Average weight × Number of students = 163 pounds × 97 = 15,811 pounds
Next, we find the sum of the weights of both groups to determine the total weight of all 100 students:
- Total weight of all students = Total weight of group 1 + Total weight of group 2 = 405 pounds + 15,811 pounds = 16,216 pounds
To find the overall average weight, we divide the total weight of all students by the total number of students:
- Overall average weight = Total weight of all students / Total number of students
- Overall average weight = 16,216 pounds / 100 students = 162.16 pounds
By rounding to the nearest whole number, we get an overall average weight of 162 pounds.
Answer: 162
Explanation
The formula to use is [tex]m = \frac{S}{n}[/tex] where S is the sum of the values and n is the number of values.
The first portion "The average weight of the first 3 students was 135 pounds" has us go from [tex]m = \frac{S}{n}[/tex] to [tex]135 = \frac{S}{3}[/tex] and that solves to S = 405.
The first three students have a combined weight of 405 pounds.
Using the same logic, the next 97 students will have a combined weight of 15811 pounds.
In total, all 100 students have a combined weight of 405+15811 = 16216 pounds. Divide that over 100 to get the overall average.
16216/100 = 162.16 which rounds to 162 and it is the final answer.
Here's another approach.
(3/100)*135 + (97/100)*163 = 162.16 which rounds to 162
For more information, search out "weighted average".
